33.(x -26)(53+52)/53-52=1

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5^{(x + 1)} + 5^{(2 - x)} = 5^{3} + 1

5^{x + 1} + 5^{2 - x} = 5^{3} + 1

HCF of $(2^{3} \times 3^{2} \times 5), (2^{2} \times 3^{3} \times 5^{2}) a n d (2^{4} \times 3 \times 5^{3} \times 7)$ is

(a) 30 (b) 48 (c) 60 (d)105

Find the sum of the following series to infinity :

(i) $1 - \frac{1}{3} + \frac{1}{3^{2}} - \frac{1}{3^{3}} + \frac{1}{3^{4}} + . . . . \infty$

(ii) $8 + 4 \sqrt{2} + 4 + . . . . \infty$

(iii) $\frac{2}{5} + \frac{3}{5^{2}} + \frac{2}{5^{3}} + \frac{3}{5^{4}} + . . . . . \infty$ .

(iv) 10 - 9 + 8.1 - 7.29 + ...... $\infty$

(v) $\frac{1}{3} + \frac{1}{5^{2}} + \frac{1}{3^{3}} + \frac{1}{5^{4}} + \frac{1}{3^{5}} + \frac{1}{5^{6}} + . . . . . \infty$

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